From what I understand you have complete control of your being/body. You can refuse any type of procedure. You are responsible for your own decisions. Of course if you are incapacitated the medical community has a responsibility to do what is necessary in that situation on test/surgeries....which is another topic (another reason to have medical power of attorney with a spouse or responsible party).
On to clarify the CT scan/pet scan. Most of us that have had high grade and many with low grade tumors on this board have had one or the other. The CT scan is more prevalent, I believe. The jury is out on radiation as possibly causing problems or the contrast dye. At the same time, these tests do help ID either a clear situation or ID more involvement in the tissues. I had the CT scan with contrast 12+ years ago and have had no further problems. It did help ID a small, papillary tumor. In general, I consider these valuable tools.